KTV歌曲推荐-因子分解机和DeepFM

前言

今天应该是推荐算法的最后一篇了，因子分解机deepFM。此处跳过了FM和FFM，因为我马上要去干别的了，所以直接用deepFM收尾吧。 先po两篇论文

• FM论文
• deepFM论文

看完这两篇论文，基本就能理解FM和DeepFM了。为了节省大家的时间我简述一下一些基本思想。

FM因子分解机

在FM出现以前大多使用SVM来做CTR预估，当然还有其他的比如SVD++,PITF，FPMC等，但是这些模型对稀疏矩阵显得捉襟见肘，而且参数规模很大。 那FM解决了什么问题：

• 更适合做稀疏矩阵的参数计算
• 减少了需要训练的参数规模，而且特征和参数数量是线性关系
• FM可以使用任何真实数据进行计算

其实FM出现主要解决了特征之间的交叉特征关系，此处省略了稀疏矩阵导致的w参数失效的模型直接说最终模型：

这里通过一个向量v的交叉来解决了稀疏矩阵导致的导致参数失效的问题。 那他参数的规模为什么小呢，接下来就是推导后面二次项部分：

从这里可以看出参数的复杂度是线性的O(kn)。

Keras对FM建模

这里是单纯的FM模型代码，这代码是借鉴别人的，我发现有一个问题就是，他最后repeat了二次项，这块我不是太明白，贴出来大家有兴趣可以一起讨论。

import os
os.environ["CUDA_VISIBLE_DEVICES"]="-1"

import keras.backend as K
from keras import activations
from keras.engine.topology import Layer, InputSpec


class FMLayer(Layer):
    def __init__(self, output_dim,
                 factor_order,
                 activation=None,
                 **kwargs):
        if 'input_shape' not in kwargs and 'input_dim' in kwargs:
            kwargs['input_shape'] = (kwargs.pop('input_dim'),)
        super(FMLayer, self).__init__(**kwargs)

        self.output_dim = output_dim
        self.factor_order = factor_order
        self.activation = activations.get(activation)
        self.input_spec = InputSpec(ndim=2)

    def build(self, input_shape):
        assert len(input_shape) == 2
        input_dim = input_shape[1]

        self.input_spec = InputSpec(dtype=K.floatx(), shape=(None, input_dim))

        self.w = self.add_weight(name='one',
                                 shape=(input_dim, self.output_dim),
                                 initializer='glorot_uniform',
                                 trainable=True)
        self.v = self.add_weight(name='two',
                                 shape=(input_dim, self.factor_order),
                                 initializer='glorot_uniform',
                                 trainable=True)
        self.b = self.add_weight(name='bias',
                                 shape=(self.output_dim,),
                                 initializer='zeros',
                                 trainable=True)

        super(FMLayer, self).build(input_shape)

    def call(self, inputs, **kwargs):
        X_square = K.square(inputs)

        xv = K.square(K.dot(inputs, self.v))
        xw = K.dot(inputs, self.w)

        p = 0.5 * K.sum(xv - K.dot(X_square, K.square(self.v)), 1)

        rp = K.repeat_elements(K.expand_dims(p, 1), self.output_dim, axis=1)
        f = xw + rp + self.b

        output = K.reshape(f, (-1, self.output_dim))

        if self.activation is not None:
            output = self.activation(output)

        return output

    def compute_output_shape(self, input_shape):
        assert input_shape and len(input_shape) == 2
        return input_shape[0], self.output_dim

inp = Input(shape=(np.shape(x_train)[1],))
x = FMLayer(200, 100)(inp)
x = Dense(2, activation='sigmoid')(x)
model.compile(loss='binary_crossentropy',
                      optimizer='adam',
                      metrics=['accuracy'])

model.fit(x_train, y_train,
          batch_size=32,
          epochs=10,
          validation_data=(x_test, y_test))

运行结果

Train on 2998 samples, validate on 750 samples
Epoch 1/10
2998/2998 [==============================] - 2s 791us/step - loss: 0.0580 - accuracy: 0.9872 - val_loss: 0.7466 - val_accuracy: 0.8127
Epoch 2/10
2998/2998 [==============================] - 2s 683us/step - loss: 0.0650 - accuracy: 0.9893 - val_loss: 0.7845 - val_accuracy: 0.8067
Epoch 3/10
2998/2998 [==============================] - 2s 674us/step - loss: 0.0803 - accuracy: 0.9915 - val_loss: 0.8730 - val_accuracy: 0.7960
Epoch 4/10
2998/2998 [==============================] - 2s 681us/step - loss: 0.0362 - accuracy: 0.9943 - val_loss: 0.8771 - val_accuracy: 0.8013
Epoch 5/10
2998/2998 [==============================] - 2s 683us/step - loss: 0.0212 - accuracy: 0.9953 - val_loss: 0.9035 - val_accuracy: 0.8007
Epoch 6/10
2998/2998 [==============================] - 2s 721us/step - loss: 0.0188 - accuracy: 0.9965 - val_loss: 0.9295 - val_accuracy: 0.7993
Epoch 7/10
2998/2998 [==============================] - 2s 719us/step - loss: 0.0168 - accuracy: 0.9972 - val_loss: 0.9597 - val_accuracy: 0.8007
Epoch 8/10
2998/2998 [==============================] - 2s 693us/step - loss: 0.0150 - accuracy: 0.9973 - val_loss: 0.9851 - val_accuracy: 0.7993
Epoch 9/10
2998/2998 [==============================] - 2s 677us/step - loss: 0.0137 - accuracy: 0.9972 - val_loss: 1.0114 - val_accuracy: 0.7987
Epoch 10/10
2998/2998 [==============================] - 2s 684us/step - loss: 0.0126 - accuracy: 0.9977 - val_loss: 1.0361 - val_accuracy: 0.8000

FFM算法

上面FM算法也可以看出来只是有一组特征，但是现实生活中可能会有多组特征，例如论文中举例：

此处包含了用户，电影，用户打分的其他电影，时间信息等，所以光是一组特征的交叉还不够，可能涉及到不同组特征的交叉。所以FFM应运而生。此处不详细介绍，直接说deepFM。

DeepFM算法

DeepFM一样我就不详细介绍了，不明白的自己看上面论文，我直说重点。

DeepFM的优点

• 结合了FM和DNN，结合了高阶特征建模DNN和低阶特征建模FM
• DeepFM低阶部分和高阶部分共享了相同的特征，让计算更有效率
• DeepFM在CTR预测中效果最好

DeepFM网络结构

FM部分网络结构

FM部分就是把一次项和二次项结合到一起就好

# 一次项
fm_w_1 = Activation('linear')(K.dot(inputs, self.fm_w))

# 二次项
dot_latent = {}
dot_cat = []
for i in range(1, self.num_fields):
    print(self.num_fields)
    dot_latent[i] = {}
    for f in self.field_combinations[i]:
        print(len(self.field_combinations))
        dot_latent[i][f] = Dot(axes=-1, normalize=False)([latent[i], latent[f]])
        dot_cat.append(dot_latent[i][f])
print(dot_cat)
fm_w_2 = Concatenate()(dot_cat)
# Merge 一次和二次项得到FM
fm_w = Concatenate()([fm_w_1, fm_w_2])

DNN部分网络结构

DNN部分比较简单

# 加俩隐藏层
deep1 = Activation('relu')(K.bias_add(K.dot(ConcatLatent,self.h1_w),self.h1_b))
deep2 = Activation('relu')(K.bias_add(K.dot(deep1, self.h2_w), self.h2_b))

整体网络结构

这里先做Embeding，然后给DNN和FM提供数据，代码如下：

# 不同fields组合
for i in range(1, self.num_fields + 1):
    sparse[i] = Lambda(lambda x: x[:, self.id_start[i]:self.id_stop[i]],
                               output_shape=((self.len_field[i],)))(inputTensor)
    latent[i] = Activation('linear')(K.bias_add(K.dot(sparse[i],self.embed_w[i]),self.embed_b[i]))

# merge 不同 field
ConcatLatent = Concatenate()(list(latent.values()))

DeepFM代码

整体代码如下：

from keras.layers import Dense, Concatenate, Lambda, Add, Dot, Activation
from keras.engine.topology import Layer
from keras import backend as K

class DeepFMLayer(Layer):
    def __init__(self, embeddin_size, field_len_group=None, **kwargs):
        self.output_dim = 1
        self.embedding_size = 10
        self.input_spec = InputSpec(ndim=2)

        self.field_count = len(field_len_group)
        self.num_fields = len(field_len_group)
        self.field_lengths = field_len_group
        self.embed_w = {}
        self.embed_b = {}
        self.h1 = 10
        self.h2 = 10

        def start_stop_indices(field_lengths, num_fields):
            len_field = {}
            id_start = {}
            id_stop = {}
            len_input = 0

            for i in range(1, num_fields + 1):
                len_field[i] = field_lengths[i - 1]
                id_start[i] = len_input
                len_input += len_field[i]
                id_stop[i] = len_input

            return len_field, len_input, id_start, id_stop

        self.len_field, self.len_input, self.id_start, self.id_stop = \
            start_stop_indices(self.field_lengths,self.num_fields)

        def Field_Combos(num_fields):
            field_list = list(range(1, num_fields))
            combo = {}
            combo_count = 0
            for idx, field in enumerate(field_list):
                sub_list = list(range(field + 1, num_fields + 1))
                combo_count += len(sub_list)
                combo[field] = sub_list

            return combo, combo_count

        self.field_combinations, self.combo_count = Field_Combos(self.num_fields)
        print(field_len_group)
        print(self.field_combinations)
        print(self.num_fields)
        super(DeepFMLayer, self).__init__(**kwargs)

    def build(self, input_shape):
        assert len(input_shape) == 2
        total_embed_size = 0

        self.input_spec = InputSpec(dtype=K.floatx(), shape=(None, input_shape[1]))


        for i in range(1, self.num_fields + 1):
            input_dim = self.len_field[i]
            _name = "embed_W" + str(i)
            self.embed_w[i] = self.add_weight(shape=(input_dim, self.embedding_size), initializer='glorot_uniform', name=_name)
            _name = "embed_b" + str(i)
            self.embed_b[i] = self.add_weight(shape=(self.embedding_size,), initializer='zeros', name=_name)
            total_embed_size += self.embedding_size


        self.fm_w = self.add_weight(name='fm_w', shape=(input_shape[1], 1), initializer='glorot_uniform', trainable=True)


        self.h1_w = self.add_weight(shape=(total_embed_size, self.h1), initializer='glorot_uniform', name='h1_w')
        self.h1_b = self.add_weight(shape=(self.h1,), initializer='zeros', name='h1_b')

        self.h2_w = self.add_weight(shape=(self.h1, self.h2), initializer='glorot_uniform', name='h2_W')
        self.h2_b = self.add_weight(shape=(self.h2,), initializer='zeros', name='h2_b')
        self.w = self.add_weight(name='w', shape=(self.h2, 1), initializer='glorot_uniform', trainable=True)
        self.b = self.add_weight(name='b', shape=(1,), initializer='zeros', trainable=True)

        super(DeepFMLayer, self).build(input_shape)

    def call(self, inputs):
        latent = {}
        sparse = {}
        # 不同fields组合
        for i in range(1, self.num_fields + 1):
            sparse[i] = Lambda(lambda x: x[:, self.id_start[i]:self.id_stop[i]],
                                       output_shape=((self.len_field[i],)))(inputTensor)
            latent[i] = Activation('linear')(K.bias_add(K.dot(sparse[i],self.embed_w[i]),self.embed_b[i]))

        # merge 不同 field
        ConcatLatent = Concatenate()(list(latent.values()))

        # 加俩隐藏层
        deep1 = Activation('relu')(K.bias_add(K.dot(ConcatLatent,self.h1_w),self.h1_b))
        deep2 = Activation('relu')(K.bias_add(K.dot(deep1, self.h2_w), self.h2_b))

        # 一次项
        fm_w_1 = Activation('linear')(K.dot(inputs, self.fm_w))

        # 二次项
        dot_latent = {}
        dot_cat = []
        for i in range(1, self.num_fields):
            print(self.num_fields)
            dot_latent[i] = {}
            for f in self.field_combinations[i]:
                print(len(self.field_combinations))
                dot_latent[i][f] = Dot(axes=-1, normalize=False)([latent[i], latent[f]])
                dot_cat.append(dot_latent[i][f])
        print(dot_cat)
        fm_w_2 = Concatenate()(dot_cat)
        # Merge 一次和二次项得到FM
        fm_w = Concatenate()([fm_w_1, fm_w_2])

        fm = Lambda(lambda x: K.sum(x, axis=1, keepdims=True))(fm_w)

        deep_wx = Activation('linear')(K.bias_add(K.dot(deep2, self.w),self.b))
        print('build finish')
        return Add()([fm, deep_wx])

    def compute_output_shape(self, input_shape):
            return (input_shape[0], self.output_dim)


inputTensor = Input(shape=(np.shape(x_train)[1],))
deepFM_out = DeepFMLayer(10, {0:10, 1:10, 2:np.shape(x_train)[1]-20})(inputTensor)
out = Dense(2, activation="sigmoid", trainable=True)(deepFM_out)
model = Model(inputTensor, out)

model.compile(loss='binary_crossentropy',
                      optimizer='adam',
                      metrics=['accuracy'])

model.fit(x_train, y_train,
                  batch_size=32,
                  epochs=10,
                  validation_data=(x_test, y_test))

运行结果：

Train on 2998 samples, validate on 750 samples
Epoch 1/10
2998/2998 [==============================] - 1s 425us/step - loss: 0.6403 - accuracy: 0.6344 - val_loss: 0.5578 - val_accuracy: 0.7533
Epoch 2/10
2998/2998 [==============================] - 1s 226us/step - loss: 0.4451 - accuracy: 0.8721 - val_loss: 0.4727 - val_accuracy: 0.8240
Epoch 3/10
2998/2998 [==============================] - 1s 215us/step - loss: 0.2469 - accuracy: 0.9445 - val_loss: 0.5188 - val_accuracy: 0.8360
Epoch 4/10
2998/2998 [==============================] - 1s 200us/step - loss: 0.1319 - accuracy: 0.9678 - val_loss: 0.6488 - val_accuracy: 0.8233
Epoch 5/10
2998/2998 [==============================] - 1s 211us/step - loss: 0.0693 - accuracy: 0.9843 - val_loss: 0.7755 - val_accuracy: 0.8247
Epoch 6/10
2998/2998 [==============================] - 1s 225us/step - loss: 0.0392 - accuracy: 0.9932 - val_loss: 0.9234 - val_accuracy: 0.8187
Epoch 7/10
2998/2998 [==============================] - 1s 204us/step - loss: 0.0224 - accuracy: 0.9967 - val_loss: 1.0437 - val_accuracy: 0.8200
Epoch 8/10
2998/2998 [==============================] - 1s 190us/step - loss: 0.0163 - accuracy: 0.9972 - val_loss: 1.1618 - val_accuracy: 0.8173
Epoch 9/10
2998/2998 [==============================] - 1s 190us/step - loss: 0.0106 - accuracy: 0.9980 - val_loss: 1.2746 - val_accuracy: 0.8147
Epoch 10/10
2998/2998 [==============================] - 1s 213us/step - loss: 0.0083 - accuracy: 0.9987 - val_loss: 1.3395 - val_accuracy: 0.8167
Model: "model_19"

结论

从上面结果上看其实纯FM和DeepFM的在我的数据集上结果差不多，甚至跟LR也没太大差别，可能是因为我的数据集比较小。有问题可以一起讨论，希望大家好好看看论文。以上都是我的一些拙见，还望抛砖引玉。